Air separation plants produce both gaseous and liquid nitrogen, oxygen, and argon, for example, by cryogenic distillation. When a liquid product is generated, it is traditionally stored in large cryogenic storage tanks until it is needed. When needed, the liquid product is withdrawn from the cryogenic liquid storage tank and shipped to a customer or series of customers from the plant site via trucks or other shipping means. In contrast to liquid products, gaseous products are co-produced and typically sent to customers via a pipeline. The demand for liquid and/or gaseous products can vary, thus, plant rates are adjusted to meet such demands.
The costs incurred to supply such products to customers include the production cost to make the product and the distribution cost to supply that customer. Traditionally, a significant portion of the production cost is the electricity costs charged by the utility company. These electricity costs can be highly variable with price changes happening as frequently as every fifteen minutes in some areas. The electricity costs, therefore, constitute a highly variable production cost for a network of air separation plants.
Once the product has been produced, the product is then typically supplied to a large number of customers in a specific geography. The production and delivery of products from multiple production sites in a region, or continent, to multiple customers is a common optimization problem faced by many companies. In particular, the optimization of the coupled problem of determining production plans at a multitude of production sites along with determining sourcing plans to meet predicted and requested customer demands is challenging. The highly variable production cost, noted above, coupled with different production capabilities and efficiencies for each plant as well as the variability in customer demands, makes liquid production decisions and customer sourcing decisions quite complex for a network of plants and customers. In these cases, the distribution problem is often tightly coupled to the production and/or storage scheme: where and when should the product be manufactured and stored in order to facilitate the lowest total cost of production, storage, and delivery?
In the case of a network of plants producing a commodity product (e.g., liquid oxygen, liquid nitrogen, liquid argon, etc.) and then supplying the product to customers via a distribution network, there are infinite feasible scenarios for production rates at each plant since each plant can make varying amounts of each product within a given range. Simultaneously, on the distribution side, all available plant sources are taken into account when making sourcing decisions. These factors among others can lead to an exorbitant size in the combined production-distribution optimization problem where the intent is to minimize production and distribution costs and/or maximize profits for a network of plants and customers. Hence the overall network optimization problem becomes difficult to solve in even a reasonable timeframe because of the large combinatorial optimization problem.
Efforts to reduce the size of the problem on the production side have typically considered an individual plant operation without significant integration into the entire network. In other words, the plants are run over a narrow range based on constraints and past experience with those production ranges and/or plant operation is based on an optimal point of operation for that specific plant resulting in a solution that is sub-optimal network wide. In general, efforts to reduce the number of variables on the distribution side have not been made since the distribution optimization problem by itself can be solved in reasonable timeframes using current optimization systems. However, prevalent solutions still consider all possible plants as production sources, thereby increasing the problem size. In addition, some of the suggested solutions might be impractical to implement owing to constraints such as customer preference, contractual factors, etc.
Traditional approaches to the network optimization problem have mostly handled the production optimization problem and the distribution optimization problem separately in order to reduce the problem size to a manageable number of variables and get a solution in a reasonable time frame. For example, in U.S. Patent Application No. US 2006 0241986, a Genetic Algorithm was used to determine optimal production at source plants and a separate Ant Colony optimizer was used to determine optimal distribution solutions. The outputs from both optimizers were compared separately using a third optimization co-ordination module that ran a simulation to evaluate the effectiveness of different solutions suggested by each individual optimizer.
The resulting solutions are, however, sub-optimal because the whole decision space of combined production and distribution scenarios is not considered simultaneously. Many times, a sub-optimal approach like the one just described may be followed by companies who have already invested large sums of money for stand-alone optimizers to do either the production optimization or distribution optimization separately and adding a third optimizer on top is the most cost-effective option, albeit not the one that gives the most optimal solution to the combined production and distribution optimization problem itself.
Methods described in the literature also use various optimization algorithms to solve network optimization problems. One approach to solving these types of network optimization problems is discussed in U.S. Pat. No. 7,092,893, where the control of liquid production in a network of air separation plants and customers was performed using a mixed-integer non-linear programming (MINLP) technique. MINLP typically suffers from two main limitations when applied to these types of network optimization problems: (1) MINLP does not have the flexibility to solve for intermediate solutions in a reasonable time frame; and (2) when new or intermediate data is available, the only way to incorporate that new data is to run the entire optimization sequence again from the beginning. This inability to include new data from a variety of incoming data feeds as well as making intermediate solutions available are big impediments for MINLP to be used to solve network optimization problems in the most efficient, implementable, and optimized fashion. The other limitation of MINLP is that the solution obtained without the use of the new or intermediate data might also be incorrect to implement, since the situation might have changed substantially during the time it takes for the optimizer to run. Hence, the solution obtained without incorporating the latest data may not lead to the minimum cost and/or the maximum profit.
The industry has used Genetic algorithms (GA) for optimization for a long time and for a variety of applications. GA refers to a method of solving optimization problems based on a natural selection process similar to the Darwinian process of biological evolution. Starting with an initial or seed population of potential solutions, the GA selects the best or “fittest” solutions to pass along to the next step. At each step, or generation, the GA selects individuals from the population to generate new solutions and eventually evolves toward an optimal solution. The GA can be applied to most optimization problems, but is best suited to optimization problems where the objective function is discontinuous or non-linear. In the case of network optimization for producing and distributing products, including liquid products, from a number of plants to a number of customers, the electricity contracts/costs are highly non-linear. Different exemplary applications of GA include, for example, U.S. Pat. No. 7,693,653, where a GA is disclosed to dynamically determine optimal paths for unmanned vehicles to complete military missions. Also in U.S. Pat. No. 7,065,420, GA is used to determine optimal aspects of parts in the CAD design phase, thereby assessing their feasibility in the manufacturing phase. Use of GA has also been applied in Supply Chain Management problems. For example, in U.S. Pat. No. 7,643,974, use of a GA to determine optimal sourcing in a pipeline system is disclosed.
While computational power has increased to the point that elaborate optimization techniques have become practical for use in some industries, optimization of large networks is still very computationally taxing. Often, resulting solutions can take an inordinately long time to solve and may not even be applicable at a later time period owing to fluctuation in the input data, which goes into the optimization problem. In the case of supply chain management of very large distribution networks where there are numerous sourcing and customer sites, and, therefore, billions of potential scenarios exist, the amount of time for an optimal solution to be generated will exceed the time period in which it can be practically implemented.
Thus, there is a need in the art for an optimization routine to solve the combined production and distribution problem that has the flexibility to incorporate data as it becomes available and will yield intermediate solutions for quick decision making. Also there is a need to reduce the size of the problem, i.e., reduce the number of decisions that the optimizer must make, but at the same time, the optimizer result must be a practical, implementable solution.